There is no recommended standard treatment for relapsed or refractory acute myelogenous leukemia in older patients. Cytarabine is the most commonly used drug to treat these patients. This study will determine if there is benefit by combining clofarabine with cytarabine. Patients will be randomized to receive up to 3 cycles of treatment with either placebo in combination with cytarabine or clofarabine in combination with cytarabine. Randomization was stratified by remission status following the first induction regimen (no remission [i.e., CR1 = refractory] or remission <6 months vs CR1 = remission ≥6 months). CR1 is defined as remission after first pre-study induction regimen. The safety and tolerability of clofarabine in combination with cytarabine and cytarabine alone will be monitored throughout the study.